1. Field of the Invention
The present invention concerns an iterative tomosynthesis method that uses an iterative maximum a posteriori reconstruction, and in particular the analytical determination of the parameters of a prior function used in maximum a posteriori iterative reconstruction.
2. Description of the Prior Art
In tomosynthesis, a three-dimensional image is generated from a number of two-dimensional images. By means of an x-ray device with an x-ray source and a detector, a two-dimensional image or a projection of the tissue to be examined is generated from each position of x-ray source trajectory. Each two-dimensional image depicts the attenuation of the tissue in the volume that the beam has propagated through. A second two-dimensional image or a second projection of the same tissue is acquired after the beam source and/or the detector have been moved into a second position. After a number of such two-dimensional images have been acquired, a three-dimensional tomosynthesis image can be generated by means of a reconstruction. The present invention can be used in three-dimensional tomosynthesis in an x-ray technique, computed tomography, or in magnetic resonance tomography.
One field of application of the aforementioned three-dimensional imaging method is mammography. An image generation device typically used in mammography has a pivotable x-ray source and a stationary x-ray detector. The tissue to be examined is positioned over the stationary detector. The x-ray source is subsequently panned in multiple steps, for example in a range of +/−25°, and a number of two-dimensional x-ray images respectively from different pan positions of the x-ray source are acquired with the stationary detector. Naturally, it is also possible to use a number of stationary x-ray sources or to only shift the x-ray source in translation. The detector also be shifted or panned counter to the movement of the x-ray source. A three-dimensional image is generated by means of reconstruction from the plurality of two-dimensional x-ray images. Known imaging methods and devices for mammography are described in DE 10 2006 046 741 A1, DE 10 2008 004 473 A1 and DE 10 2008 028 387 A1, for example.
In the prior art a technique known as filtered back-projection is used to reconstruct a three-dimensional image from a number of two-dimensional images. Filtered back-projection is described in Imaging Systems for Medical Diagnostics, Arnulf Oppelt, Publicis Corporate Publishing, Erlangen, ISBN 3-89578-226-2, Chapter 10.5. These filtered back-projection reconstruction methods depict reconstructed images with a high contrast and a high degree of accuracy of detail but, in tomosynthesis with a limited scan angle, lose information about the relative tissue density due to the missing data. This happens in part because specific filter kernels remove low-frequency portions. In general, digital breast tomosynthesis (DBT) is negatively affected by incomplete data and a poor quantum statistic that is limited by the total dose that is absorbed in the breast. The breast is composed primarily of glandular tissue, adipose tissue, connective tissue and blood vessels. The coefficients of x-ray attenuation of these tissue type are very similar, which significantly hinders the evaluation of three-dimensional mammography images. The primary field of application of imaging methods in mammography is the early detection of cancerous tissue. This is made even more difficult because cancerous tissue has a coefficient of x-ray attenuation that is similar to that of other tissue types. Mammography methods are described in Imaging Systems for Medical Diagnostics, Arnulf Oppelt, Chapter 12.6, Publicis Corporate Publishing, Erlangen, ISBN 3-89578-226-2.
An additional problem of the aforementioned filtered back-projection reconstruction methods is that artifacts outside of the plane where the object is in focus (known as out-of-plane artifacts) are intensified by the filtering together with the image features. Statistical, iterative reconstruction methods have been suggested that maximize the similarities between the calculated and measured projections and enable a noise suppression, for example by prior functions.
Techniques known as maximum likelihood methods are employed, with which the estimated value μ of the attenuation coefficients (for example the breast volume attenuation coefficients) can be determined that maximizes the logarithmic probability function L(μ):
            μ      max        =                            arg          ⁢                                          ⁢          max                μ            ⁢              {                  L          ⁡                      (            μ            )                          }              ;
The maximum likelihood reconstruction leads to comparably good results in DBT and converges in 4 to 5 iterations. One disadvantage of such reconstructions is that excessively noisy images arise without the use of prior functions or penalty functions. The use of smoothing prior functions has been proposed. The logarithmic probability function L(μ) is hereby changed into a log posterior function:Φ(μ)=L(μ)−βU(μ);wherein U(μ) is a smoothing prior function that reduces or, respectively, penalizes the differences of the values of adjacent pixels. The parameter β>0 is a control parameter.
However, one disadvantage of this method is that the optimal parameters of the prior functions must be empirically determined, which typically comprises a search across a large value range which is undesirable given high-resolution images, in particular if multiple prior functions must be assessed.